Thermal behavior of effective U_A(1) anomaly couplings in reflection of higher topological sectors

Abstract

Thermal behavior of effective, chiral condensate-dependent $U_A(1)$ anomaly couplings is investigated using the functional renormalization group approach in the $N_f=3$ flavor meson model. We derive flow equations for anomaly couplings that arise from instantons of higher topological charge, dependent also on the chiral condensate. These flow equations are solved numerically for the $|Q|=1,2$ topological sectors at finite temperature. Assuming that the anomaly couplings at the ultraviolet scale may also exhibit explicit temperature dependence, we calculate the thermal behavior of the effective potential. In accordance with our earlier study, [G. Fejos and A. Patkos, Phys. Rev. D{\bf 105}, 096007 (2022)], we find that for increasing temperatures, the anomalous breaking of chiral symmetry tends to strengthen toward the pseudocritical temperature ($T_C$) of chiral symmetry breaking. It is revealed that below $T_C$, around $\sim$10\% of the $U_A(1)$ breaking arises from the $|Q|=2$ topological sector. Correspondingly, a detailed analysis on the thermal behavior of the mass spectrum is also presented.

11 pages, 8 figures, matches published version

References in corpus (15)

• Exact evolution equation for the effective potential
• The QCD transition temperature: results with physical masses in the continuum limit
• Chiral symmetry breaking in continuum QCD
• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• On the strength of the $U_A(1)$ anomaly at the chiral phase transition in $N_f=2$ QCD
• The Chiral Phase Transition in three-flavor QCD from Lattice QCD
• Eigenvalue spectra of QCD and the fate of $U_A(1)$ breaking towards the chiral limit
• QCD phase transitions in the light quark chiral limit
• Effects of the anomaly on the two-flavor QCD chiral phase transition
• Topological susceptibility of pure gauge theory using Density of States
• Second order chiral phase transition in three flavor quantum chromodynamics?
• Fluctuation induced first order phase transition in U(n)xU(n) models using chiral invariant expansion of functional renormalization group flows
• Fate of the topological susceptibility in two-color dense QCD
• Spectral function of the ${\eta }^{\prime }$ meson in nuclear medium based on phenomenological models
• Correlated Dirac eigenvalues around the transition temperature on $N_{\tau }=8$ lattices

Cited by in corpus (1)

• Range of topological fluctuations in the three-flavor linear sigma model